Wireless Network Transmission Through Brick Wall

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Homework Statement

A wireless computer network transmits data across the space between nodes as a modulation of a 2.45GHz (microwave) carrier signal. The signal is able to pass through a brick wall that is 100mm thick. Measurements have determined that the dielectric function at microwave frequencies for the material of a typical building brick is epsilon=epsilon(real) +i epsilon(imaginary)=5.86+0.68i, and the relative permeability is unity.

a) show that about 17 percent of the energy that strikes a brick surface at normal incidence is reflected. (since epsilon(real)>>epsilon(imaginary), it is satisfactory at the interface to suppose that epsilon is approximately epsilon(real).
b) show that in passing perpendicularly through 100mm of brick only about 16 percent of the incident energy emerges. (Multiple reflections can be ignored but transmission across both interfaces must be taken into account.)

The Attempt at a Solution

a) I've done this question. by (r_parallel)^2=R

and using the Fresnel relation. I just wondered though, if epsilon is approximately epsilon(real) should still be assumed for part b).

for part b):

I tried n=1, n'=sqrt(5.86) and substituting in those values into the equation for t_parallel, I get

air to brick:

t_parallel=0.585

brick to air

t_parallel=1.415

I don't know how to deal with the fact that t>> 1 for glass to air.

(0.585^2)*(1.415)^2 does not equal 16 percent.

I then tried to think about this logically.

100-17 percent is transmitted from air to glass.

but if I look at the reflection coefficient, it is negative from brick to air and I don't know how to deal with this. Please help.

 

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Can I say that T(brick to air)=1-T(air to brick)

because if I can, then I get the right answer to the question.

Is this just a coincidence.

If I can say that T(brick to air)=1-T(air to brick), then why is this allowed? If I try to work out T the usual way, T(air to brick)=T(brick to air), giving not the correct answer